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Electrical and Computer Engineering Dennis Goeckel University of Massachusetts Amherst This work is supported by the National Science Foundation under Grants CNS-1019464, CCF-1249275, and ECCS-1309573. Everlasting Security and Undetectability in Wireless Communications ICNC Lecture February 6, 2014

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2 Electrical and Computer Engineering Motivation Everlasting Secrecy: We are interested in keeping something secret forever. A challenge of cryptography (e.g. the VENONA project) is that recorded messages can be deciphered later. Undetectability: 1. A stronger form of security than any encryption: computational or information-theoretic. 2.Often more important than encryption: whom is talking to whom (so called “metadata”) From: The Guardian

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3 Electrical and Computer Engineering The Alice-Bob-Eve Scenario in Wireless AliceBob Eve Building It might be Eve in the parking lot listening, or…. …it might be Eve in the building! Important Challenge: the “near Eve” problem… …and you very likely will not know where she is.

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4 Electrical and Computer Engineering Computational Security (Cryptography) Eve can see the transmitted bits perfectly, but cannot solve the “hard” problem presented to her. Advantages: 1.Well-studied and efficient algorithms 2.Does not suffer from the “Near Eve” problem Disadvantages: 1.Implementations often broken (although the primitive is fine) 2.Computational assumptions on Eve 3.Message can be stored and decrypted later

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5 Electrical and Computer Engineering Information-theoretic secrecy Information is encoded in such a way that Eve gets no information about the message…if the scenario is right Advantages: 1.No computational assumptions on Eve. 2.If the transmission is securely made, it is secure forever. Disadvantages (key part of this talk): Information-theoretic secrecy generally relies on a (known) advantage for Bob over Eve (e.g. less noisy). If that is not true, Eve gets the message today. Many would argue that we have traded a long-term computational risk for a short-term scenario risk…no thank you!

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6 Electrical and Computer Engineering Outline 1.Computational and Information Theoretic security basics a.Computation Security: Diffie-Hellman b.IT Security: The wiretap channel (Wyner et al) c.Application to wireless…and challenges 2.Potential solutions a. Exploiting fading b. Two-way communications c.Attacking the receiver’s hardware d.Cooperative jamming 3.Asymptotically-large networks a.Cooperative jamming b.Network coding 4.Undetectable communications (LPD) a.Steganography b.Emerging approaches for wireless channels 5.Current and Future Challenges t P AB P AE P AB >P AE

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7 Electrical and Computer Engineering Outline 1.Computational and Information Theoretic security basics a.Computation Security: Diffie-Hellman b.Information-Theoretic Security: The wiretap channel (Wyner et al) c.Application to wireless…and challenges 2.Potential solutions a. Exploiting fading b. Two-way communications c.Attacking the receiver’s hardware d.Cooperative jamming 3.Asymptotically-large networks a.Cooperative jamming b.Network coding 4.Undetectable communications (LPD) a.Steganography b.Emerging approaches for wireless channels 5.Current and Future Challenges S Alice Bob

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8 Electrical and Computer Engineering Outline 1.Computational and Information Theoretic security basics a.Computation Security: Diffie-Hellman b.Information-Theoretic Security: The wiretap channel (Wyner et al) c.Application to wireless…and challenges 2.Potential solutions a. Exploiting fading b. Two-way communications c.Attacking the receiver’s hardware d.Cooperative jamming 3.Asymptotically-large networks a.Cooperative jamming b.Network coding 4.Undetectable communications (LPD) a.Steganography b.Emerging approaches for wireless channels 5.Current and Future Challenges

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9 Electrical and Computer Engineering Outline 1.Computational and Information Theoretic security basics a.Computation Security: Diffie-Hellman b.Information-Theoretic Security: The wiretap channel (Wyner et al) c.Application to wireless…and challenges 2.Potential solutions a. Exploiting fading b. Two-way communications c.Attacking the receiver’s hardware d.Cooperative jamming 3.Asymptotically-large networks a.Cooperative jamming b.Network coding 4.Undetectable communications (LPD) a.Emerging approaches for wireless b.Experiments 5.Current and Future Challenges

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10 Electrical and Computer Engineering Outline 1.Computational and Information Theoretic security basics a.Computation Security: Diffie-Hellman b.Information-Theoretic Security: The wiretap channel (Wyner et al) c.Application to wireless…and challenges 2.Potential solutions a. Exploiting fading b. Two-way communications c.Attacking the receiver’s hardware d.Cooperative jamming 3.Asymptotically-large networks a.Cooperative jamming b.Network coding 4.Undetectable communications (LPD) a.Emerging approaches for wireless channels b.Experiments 5.Current and Future Challenges

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11 Electrical and Computer Engineering Outline 1.Computational and Information Theoretic security basics a.Computation Security: Diffie-Hellman b.Information-Theoretic Security: The wiretap channel (Wyner et al) c.Application to wireless…and challenges 2.Potential solutions 3.Asymptotically-large networks 4.Undetectable communications (LPD) 5.Current and Future Challenges t P AB P AE P AB >P AE

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12 Electrical and Computer Engineering Diffie-Hellman: Establishing a key “on the fly” AliceBob Eve Set-up: Alice announces a large prime p and a primitive root g mod p. 1.Alice chooses a secret random integer a, 1 < a < p-1, and broadcasts y a =g a mod p. 2. Bob chooses a secret random integer b, 1 < b < p-1, and broadcasts y b =g b mod p. yaya ybyb 3.Alice forms the key K=y b a mod p =g ab mod p 3.Bob forms the key K=y a b mod p =g ab mod p Eve is left trying to solve the discrete logarithm problem, which is believed to be “hard”. I. Comp and IT security basics: (a) Diffie-Hellman (b) The wiretap channel (c) Wireless

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13 Electrical and Computer Engineering Diffie-Hellman: An Example AliceBob Eve Set-up: Alice announces a large prime p=19 and a primitive root g=2. 1.Alice chooses a secret random integer a=5, 1 < a < 18, and broadcasts y a =2 5 mod 19=13. 2. Bob chooses a secret random integer 6, 1 < b < 18, and broadcasts y b =2 6 mod 19=7. yaya ybyb 3. Alice forms the key: K=7 5 mod 19=11 3.Bob forms the key: K=13 6 mod 19=11 Eve is left trying to solve the discrete logarithm problem, which is believed to be “hard”. From: J. Talbot and D. Welsh, Complexity and Cryptography I. Comp and IT security basics: (a) Diffie-Hellman (b) The wiretap channel (c) Wireless

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14 Electrical and Computer Engineering Diffie-Hellman: How could it be broken? 1.The discrete logarithm is not hard (unlikely?) This motivates approaches of “keyless security”, where what the eavesdropper receives does not contain enough information to (ever) decode the message…information-theoretic secrecy. I. Comp and IT security basics: (a) Diffie-Hellman (b) The wiretap channel (c) Wireless [Courtesy: C. Paar] 2. Somebody obtains the key in some other manner (e.g. side-channel analysis on power utilization of a processor). 3. Advances in computing [from: “wired.com”]

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15 Electrical and Computer Engineering Shannon and the one-time pad [C. Shannon, 1948] Consider perfect secrecy over a noiseless wireline channel: Desire I(M,g K (M))= 0 Questions: 1.How long must K be for an N-bit message M? 2.How do you choose g K (M)? AliceBob Eve M g K (M) Pre-shared key K ? M I. Comp and IT security basics: (a) Diffie-Hellman (b) The wiretap channel (c) Wireless

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16 Electrical and Computer Engineering Shannon and the one-time pad [C. Shannon, 1948] Answers: 1.You need an N-bit key K for an N-bit message M. 2.g K (M) = M K AliceBob Eve M M K Pre-shared key K ? (M K) K = M Blah. I. Comp and IT security basics: (a) Diffie-Hellman (b) The wiretap channel (c) Wireless

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17 Electrical and Computer Engineering Example: Why not a “two-time pad”? What does Eve do? AliceBob Eve M 1,M 2 M 1 K M 2 K Pre-shared key K ? I. Comp and IT security basics: (a) Diffie-Hellman (b) The wiretap channel (c) Wireless M 1,M 2 This is an information leak of K bits! Not information-theoretic secure. (VENONA exploited this).

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18 Electrical and Computer Engineering The Wiretap Channel [Wyner, 1975; Cheong and Hellman, 1978] But suppose: 1.There is noise in the system. 2.The eavesdropper has a worse view of the transmitted signal than Bob. R AB : Capacity of channel from Alice to Bob R AE : Capacity of channel from Alice to Eve R AB > R AE AliceBob Eve Building R = log 2 (1 + SNR AB ) – log 2 (1 + SNR AE ) Gaussian channels: Positive rate “if Bob’s channel is better”, and Eve gets nothing. I. Comp and IT security basics: (a) Diffie-Hellman (b) The wiretap channel (c) Wireless

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19 Electrical and Computer Engineering Wiretap Code Construction [Wyner, 1975] 1010 10101 0101 1010 0 1010 1010 1 10101 0101 1 011 0 10101 0101 0 0 0 0 0101 10101 0101 0101 0 0101 0101 11 10 00 01 1. Alice generates random codewords. Code Book Construction: 2. She splits them randomly into bins. 3.Codebook is broadcast to everybody, including Eve I. Comp and IT security basics: (a) Diffie-Hellman (b) The wiretap channel (c) Wireless

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20 Electrical and Computer Engineering Wiretap Code Encoding 1010 10101 0101 1010 0 1010 1010 1 10101 0101 1 0 1 1 0 10101 0101 0 0 0 0 0101 10101 0101 0101 0 0101 0101 11 10 00 01 Alice picks a circle at random and uses R o information bits to pick a codeword within that circle. Alice sends. I. Comp and IT security basics: (a) Diffie-Hellman (b) The wiretap channel (c) Wireless

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21 Electrical and Computer Engineering Wiretap Code Decoding Bob’s able to decode information bits 11 corresponding to codeword 0011 Secrecy capacity is given by the difference in the capacities between the main channel and the eavesdropper channel. ? 10 11 00 01 11 10 00 01 10 11 01 10 00 10 11 1011 01 11 00 11 00 1011 01 00 01 1011 01 00 01 11 10 00 01 Bob Eve I. Comp and IT security basics: (a) Diffie-Hellman (b) The wiretap channel (c) Wireless

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22 Electrical and Computer Engineering Secrecy Outage Event Outage R S < 2 Secrecy R S >2 R S = 2 I. Comp and IT security basics: (a) Diffie-Hellman (b) The wiretap channel (c) Wireless Bob Channel Capacity Eve Channel Capacity

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23 Electrical and Computer Engineering Critical Issue in Trying to Plan Secrecy: What do we Know? AliceBob Eve R AB R AE Do we know R AB ? Maybe. Do we know R AE ? Probably not. I. Comp and IT security basics: (a) Diffie-Hellman (b) The wiretap channel (c) Wireless

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24 Electrical and Computer Engineering Known CSI to Bob (known R b puts on this line) Outage R S < 2 Secrecy R S >2 I. Comp and IT security basics: (a) Diffie-Hellman (b) The wiretap channel (c) Wireless Outage Prob = P(R E > 2.5) Bob Channel Capacity Eve Channel Capacity

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25 Electrical and Computer Engineering Wireless Channels: Path Loss d r A What happens to the transmitted wave on the way from the cell phone to the tower? Goes in all directions (broadcast) and the signal strength weakens. Let’s model it. T.S. Rappaport, Wireless Communications Note that the differences in received powers can be huge, for example, in a cell phone system: I. Comp and IT security basics: (a) Diffie-Hellman (b) The wiretap channel (c) Wireless

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26 Electrical and Computer Engineering Small Scale: Multi-path Fading What happens to the signal on the way from the cell phone to the tower? It gets reflected by many objects and the reflections add up at the receiver. Example: Two paths of different lengths, signals arrive at slightly different times. One path is 100ft longer: 100ns difference (big deal?). Carrier might be at 1 GHz -> period 1ns (So, yes, big deal) Walk around the room while you speak on the phone -> the two signals keep adding up or canceling at the receiver as you move. Key: Varies 3 ways: 1.Spatially 2.Temporally 3.With frequency I. Comp and IT security basics: (a) Diffie-Hellman (b) The wiretap channel (c) Wireless

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27 Electrical and Computer Engineering AliceBob Eve Building R = log 2 (1 + SNR AB ) – log 2 (1 + SNR AE ) Computational Security: Plus: Positive rate “if Bob’s channel is better”, and Eve gets nothing. I. Comp and IT security basics: (a) Diffie-Hellman (b) The wiretap channel (c) Wireless Drawback: Zero rate “if Eve’s channel is better”, and Bob gets nothing. Information-Theoretic Security: Drawback: “Only” computational security. Plus : No problem with the “Near Eve”. Question: Can we get the best of both worlds.

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28 Electrical and Computer Engineering Outline 1.Computational and Information Theoretic security basics 2.Potential solutions a. Exploiting fading b. Two-way communications c.Attacking the receiver’s hardware d.Cooperative jamming 3.Asymptotically-large networks 4.Undetectable communications (LPD) 5.Current and Future Challenges S Alice Bob

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29 Electrical and Computer Engineering Exploiting Fading I: signal when we have the advantage AliceBob Eve R = log 2 (1 + P AB ) – log 2 (1 + P AE ) t P AB P AE P AB >P AE P AB Potential Solutions: (a) Exploiting fading (b) 2-way comms (c) Rcvr harware (d) Jamming CSI = Path-loss and fading Situations: (1) Known CSI, (2) Partial CSI (all Bob, path-loss to Eve), (3) N o CSI Problem: If I do not know where Eve is, how do I choose a strategy/rate?

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30 Electrical and Computer Engineering Exploiting Fading II: derive a key fro m it AliceBob Eve 1.Alice broadcasts a pilot signal. Bob measures the channel H AB 2. Bob broadcasts a pilot signal. Alice measures the channel H BA 3.Assuming reciprocity, H AB =H BA, and we have a source of common randomness. Alice and Bob reconcile their channel estimates to form a common key K. 4. Alice broadcasts with a one-time pad: X=M XOR K Potential Solutions: (a) Exploiting fading (b) 2-way comms (c) Rcvr hardware (d) Jamming Drawback: Limited number of bits can be extracted

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31 Electrical and Computer Engineering Public Discussion [Maurer, 1993][Ahlswede and Csiszar, 1993] AliceBob Eve Eve is closer than Bob. Consider binary symmetric channels (0 or 1 in, 0 or 1 out): 0 0 11 1-p B pBpB pBpB 0 0 11 1-p E pEpE pEpE Bob’s Channel (p B :prob of error)Eve’s Channel (p E :prob of error) p B >p E (since Eve is closer); hence, the secrecy capacity is zero. What to do? Potential Solutions: (a) Exploiting fading (b) 2-way comms (c) Rcvr hardware (d) Jamming

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32 Electrical and Computer Engineering Public Discussion II AliceBob Eve 1. Bob transmits X: Alice Receives: Eve Receives: 2.Alice transmits (on noiseless, public channel): M Bob Receives: Eve Receives: 3.Bob forms: Eve forms: …and we have a channel of positive capacity. Potential Solutions: (a) Exploiting fading (b) 2-way comms (c) Rcvr hardware (d) Jamming But it could be a really small capacity… If Eve is close to Bob…and how do you choose the rate?

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33 Electrical and Computer Engineering Public Discussion III Problem: Rate becomes limited for a very near Eve. What if Eve picks up the transmitter? Potential Solutions: (a) Exploiting fading (b) 2-way comms (c) Rcvr hardware (d) Jamming

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34 Electrical and Computer Engineering Challenges 1.Exploiting when Alice -> Bob channel is better than Alice -> Eve Challenge: unknown Eve location 2.Exploiting common randomness of channel reciprocity Challenge: limited number of key bits 3.Exploiting “public discussion” Challenge: two-way communication and unknown Eve

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35 Electrical and Computer Engineering Cachin and Maurer introduced the “bounded memory model” to achieve everlasting secrecy [Cauchin and Maurer, 1997]. An eavesdropper with memory < M cannot store enough to eventually break the cipher. 4/12 Attacking the Hardware I: Bounded Memory Model [From “blog.dshr.org”] Potential Solutions: (a) Exploiting fading (b) 2-way comms (c) Rcvr hardware (d) Jamming 1. The density of memories grows quickly (Moore’s Law) However, it is hard to pick a memory size that Eve cannot use beyond: 2. Memories can be stacked arbitrarily subject only to (very large) space limitations.

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36 Electrical and Computer Engineering Bounded Conversion Model 1. In the combative sender-eavesdropper game, front-end dynamic range is a critical aspect of the receiver. 2. A/D Technology progresses very slowly. 3. High-end A/D’s are already stacked to the limit of the jitter. Perhaps Cachin and Maurer attacked the wrong part of the receiver: Idea: AliceBob Eve Potential Solutions: (a) Exploiting fading (b) 2-way comms (c) Rcvr hardware (d) Jamming 1. IT security requires a channe l advantage. 2.Establish cryptographic security (e.g. Diffie-Hellman) 3.Use a short-term cryptographic to establish the channel advantag e. Analog “Front-End” A/D Digital “Back-End” Eve’s Receiver [Sheikholeslami, Goeckel, Pishro-Nik, 2013]

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37 Electrical and Computer Engineering 5/12 System model and approach: Potential Solutions: (a) Exploiting fading (b) 2-way comms (c) Rcvr hardware (d) Jamming 1.Alice and Bob pre-share an “emphemeral” cryptographic key k to choose g(.). Note: Key will be handed to Eve after transmission. 2.A/D is a non-linear element. Non-commutativity of non-linear elements: potential information-theoretic security. k 3.Secrecy rate is a shaping gain: R s =E g [h(X) – h(g(X))] h(X): differential entropy …but, unlike traditional “shaping gains”, gain can be huge.

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38 Electrical and Computer Engineering 6/12 Rapid power modulation for secrecy: Potential Solutions: (a) Exploiting fading (b) 2-way comms (c) Rcvr hardware (d) Jamming Idea: Key used to rapidly power modulate transmitter. Bob’s receiver gain control can follow, while Eve’s struggles.

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39 Electrical and Computer Engineering 6/12 Rapid power modulation for secrecy: Potential Solutions: (a) Exploiting fading (b) 2-way comms (c) Rcvr hardware (d) Jamming

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40 Electrical and Computer Engineering 6/12 Rapid power modulation for secrecy: Potential Solutions: (a) Exploiting fading (b) 2-way comms (c) Rcvr hardware (d) Jamming

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41 Electrical and Computer Engineering 6/12 Rapid power modulation for secrecy: Potential Solutions: (a) Exploiting fading (b) 2-way comms (c) Rcvr hardware (d) Jamming Bob’s gain control is correct: input well-matched to A/D span.

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42 Electrical and Computer Engineering 7/12 Rapid power modulation for secrecy: Potential Solutions: (a) Exploiting fading (b) 2-way comms (c) Rcvr hardware (d) Jamming 2. It is easy to show that the optimal strategy (for Eve) is to pick a single gain G. 1.Alice sets her parameters to maximize R s, whereas Eve tries to find a gain G that minimizes the secrecy rate R s given Alice’s choice: R s =max S min G R s (S, G)

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43 Electrical and Computer Engineering Large gain Effect of A/D on the signal: Clipping (due to overflow) 8/12 Rapid power modulation for secrecy: Potential Solutions: (a) Exploiting fading (b) 2-way comms (c) Rcvr hardware (d) Jamming

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44 Electrical and Computer Engineering Small gain Effect of A/D on the signal: Clipping (due to overflow) Quantization noise (uniformly distributed ) 8/12 Rapid power modulation for secrecy: Potential Solutions: (a) Exploiting fading (b) 2-way comms (c) Rcvr hardware (d) Jamming

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45 Electrical and Computer Engineering Effect of A/D on the signal: Clipping (due to overflow) Quantization noise (uniformly distributed ) Trade-off between choosing a large gain and a small gain: Eve needs to compromise between more A/D overflows or less resolution. 8/12 Rapid power modulation for secrecy: Potential Solutions: (a) Exploiting fading (b) 2-way comms (c) Rcvr hardware (d) Jamming

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46 Electrical and Computer Engineering Potential Solutions: (a) Exploiting fading (b) 2-way comms (c) Rcvr hardware (d) Jamming (a) Public Discussion (b) Power modulation (Although they are not really competing techniques. Power modulation approach could be used under public discussion.) What if Eve picks up the transmitter?

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47 Electrical and Computer Engineering Secrecy rate vs. SNR at Bob, Eve has perfect access to the signal 10/12 Potential Solutions: (a) Exploiting fading (b) 2-way comms (c) Rcvr hardware (d) Jamming Noisy channel to Bob, noiseless channel to Eve. AliceBob Eve Challenges: (1) Only effective (so far) in short-range environments. (2) Risk Eve has a better receiver than you thought.

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48 Electrical and Computer Engineering Challenges 1.Exploiting when Alice -> Bob channel is better than Alice -> Eve Challenge: unknown Eve location 2.Exploiting common randomness of channel reciprocity Challenge: limited number of key bits 3.Exploiting “public discussion” Challenge: two-way communication and unknown Eve 4.Attacking Eve’s receiver hardware Challenge: short range, assumptions on Eve’s hardware

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49 Electrical and Computer Engineering Cooperative Jamming for Secrecy [Negi/Goel, 2005] AliceBob Eve M First paper to guarantee a minimum secrecy capacity, independent of the location of the eavesdropper. Alice’s channel state information knowledge: 1.She knows the channel to Bob 2.She does not know the channel to Eve Idea: Jam in the null space of Bob’s receiver. Problem: Asymmetric capabilities are backward! (more powerful Alice than Eve)! Potential Solutions: (a) Exploiting fading (b) 2-way comms (c) Rcvr hardware (d) Jamming

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50 Electrical and Computer Engineering Cooperative Jamming for Secrecy II [Goel/Negi, 2008] AliceBob Eve M R4R4 R5R5 1.Stage 1: Alice and Bob send “noise messages” 2.Stage 2: Alice sends the message plus a signal to cancel relay chatter. Relays “chatter” Relay chatter only affects Eve due to interference pre-cancellation by Alice. Potential Solutions: (a) Exploiting fading (b) 2-way comms (c) Rcvr hardware (d) Jamming Challenge: Interference cancellation challenging in a near-far environment.

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51 Electrical and Computer Engineering Challenges 1.Exploiting when Alice -> Bob channel is better than Alice -> Eve Challenge: unknown Eve location 2.Exploiting common randomness of channel reciprocity Challenge: limited number of key bits 3.Exploiting “public discussion” Challenge: two-way communication and unknown Eve 4.Attacking Eve’s receiver hardware Challenge: short range, assumptions on Eve’s hardware 5.Interference Cancellation Challenge: near-far environment

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52 Electrical and Computer Engineering Recall: Small Scale: Multi- path Fading Key: Varies three ways: 1.Spatially 2.Temporally 3.With frequency Potential Solutions: (a) Exploiting fading (b) 2-way comms (c) Rcvr hardware (d) Jamming

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53 Electrical and Computer Engineering 53 Could wait until channel until channel from Alice to Bob is really good… … Exploiting spatial fading : Alice Bob Potential Solutions: (a) Exploiting fading (b) 2-way comms (c) Rcvr hardware (d) Jamming

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54 Electrical and Computer Engineering 54 Could wait until channel until channel from Alice to Bob is really good… …or could look at relays, which yield a random spatial sampling of the field. For Rayleigh fading, power at “best” relay of N relays goes as P S,R * ~ log N. Alice Bob Potential Solutions: (a) Exploiting fading (b) 2-way comms (c) Rcvr hardware (d) Jamming

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55 Electrical and Computer Engineering The “Two-Hop” Case S D E2E2 E1E1 E3E3 Scenario: Source “S” wants to communicate securely with the destination “D” in the presence of M eavesdroppers (M=3 above) with the help of N relays (N=5 above). Goal: Deliver a packet from S to D of rate R, such that D “always” decodes the packet, and none of the eavesdroppers decodes the packet. Question: How many eavesdroppers can be tolerated? Alice Bob Potential Solutions: (a) Exploiting fading (b) 2-way comms (c) Rcvr hardware (d) Jamming

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56 Electrical and Computer Engineering S D E2E2 E1E1 E3E3 Approach: (Ignore path-loss for now) Find the relay R * that has the best fading gains on S -> R * and R * -> D. More precisely, Assuming an exponential tail on the magnitude squared of the fading distribution of any link, Then, can transmit with power 2/log N, and tolerate sqrt(N) eavesdroppers. Alice Bob Potential Solutions: (a) Exploiting fading (b) 2-way comms (c) Rcvr hardware (d) Jamming

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57 Electrical and Computer Engineering S D Scenario: Source “S” wants to communicate securely with the destination “D” in the presence of M eavesdroppers (M=3 above) with the help of N relays (N=5) above. Step 1: Source broadcasts pilot. Relay i measures S -> R i channel, i=0,1,…N-1. Basic Idea: If you cannot hear somebody “talk”, then, by reciprocity, they will not be able to hear you. That allows you to be a jammer with little pain to the system when that person receives. Alice Bob Potential Solutions: (a) Exploiting fading (b) 2-way comms (c) Rcvr hardware (d) Jamming

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58 Electrical and Computer Engineering S Scenario: Source “S” wants to communicate securely with the destination “D” in the presence of M eavesdroppers (M=3 above) with the help of N relays (N=5) above. Step 1: Source broadcasts pilot. Relay i measures S -> R i channel, i=0,1,…N-1. D Step 2: Destination broadcasts pilot. Relay i measures D -> R i channel, i=0,1,…N-1. Alice Bob Potential Solutions: (a) Exploiting fading (b) 2-way comms (c) Rcvr hardware (d) Jamming

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59 Electrical and Computer Engineering S Scenario: Source “S” wants to communicate securely with the destination “D” in the presence of M eavesdroppers (M=3 above) with the help of N relays (N=5) above. Step 1: Source broadcasts pilot. Relay i measures S -> R i channel, i=0,1,…N-1. D Step 2: Destination broadcasts pilot. Relay i measures D -> R i channel, i=0,1,…N-1. Step 3: “Best” relay broadcasts pilot. Relay i measures R * -> R i channel, i=0,1,…N-1. (Note that this can be done in a distributed manner, with success prob c > 0). Alice Bob Potential Solutions: (a) Exploiting fading (b) 2-way comms (c) Rcvr hardware (d) Jamming

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60 Electrical and Computer Engineering Scenario: Source “S” wants to communicate securely with the destination “D” in the presence of M eavesdroppers (M=3 above) with the help of N relays (N=5) above. Step 1: Source broadcasts pilot. Relay i measures S -> R i channel, i=0,1,…N-1. D Step 2: Destination broadcasts pilot. Relay i measures D -> R i channel, i=0,1,…N-1. Step 3: “Best” relay broadcasts pilot. Relay i measures R * -> R i channel, i=0,1,…N-1. Step 4: Source transmits message. Relays with “bad” (to be defined later) R i -> R * channels generate random noise (to confuse eavesdroppers). S Alice Bob Potential Solutions: (a) Exploiting fading (b) 2-way comms (c) Rcvr hardware (d) Jamming

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61 Electrical and Computer Engineering Scenario: Source “S” wants to communicate securely with the destination “D” in the presence of M eavesdroppers (M=3 above) with the help of N relays (N=5) above. Step 1: Source broadcasts pilot. Relay i measures S -> R i channel, i=0,1,…N-1. D Step 2: Destination broadcasts pilot. Relay i measures D -> R i channel, i=0,1,…N-1. Step 3: “Best” relay broadcasts pilot. Relay i measures R * -> R i channel, i=0,1,…N-1. Step 4: Source transmits message. Relays with “bad” R i -> R * channels generate random noise (to confuse eavesdroppers). Step 5: Relay R * transmits message. Relays with “bad” (to be defined later) R i -> D channels generate random noise (to confuse eavesdroppers). S Alice Bob Potential Solutions: (a) Exploiting fading (b) 2-way comms (c) Rcvr hardware (d) Jamming

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62 Electrical and Computer Engineering Consider how the (possible) chatter of N intermediate nodes might help us to communication secretly in the presence of Eve. Can achieve a secrecy rate R with probability 1 (over the locations of nodes) for asymptotically large N if the number of eavesdroppers satisfies: Standard MU diversity: best relay/power control Proposed Scheme: intelligent “chatter” Lower bound on Eve distance from S Uniformly distributed eavesdroppers Potential Solutions: (a) Exploiting fading (b) 2-way comms (c) Rcvr hardware (d) Jamming Problem: Convergence (in N) is slow. Not practical (we tried!). Solution (?): Use the (multi-hop) network.

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63 Electrical and Computer Engineering Challenges 1.Exploiting when Alice -> Bob channel is better than Alice -> Eve Challenge: unknown Eve location 2.Exploiting common randomness of channel reciprocity Challenge: limited number of key bits 3.Exploiting “public discussion” Challenge: two-way communication and unknown Eve 4.Attacking Eve’s receiver hardware Challenge: short range, assumptions on Eve’s hardware 5. Interference Cancellation Challenge: near-far environment 6.Relay Chattering Challenge: great in theory, not so much in practice (density of nodes).

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64 Electrical and Computer Engineering Outline 1.Computational and Information Theoretic security basics 2.Potential solutions 3.Asymptotically-large networks a.Cooperative jamming b.Network coding 4.Undetectable communications (LPD) 5.Current and Future Challenges

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65 Electrical and Computer Engineering 1.How much secret information can be shared by a network of wireless nodes in the presence of eavesdropper nodes? [Gupta/Kumar et al] The Network Scale: AliceBob Eve So far we have considered: But now we want to consider: 2.… and how many eavesdroppers can the network tolerate? Questions: Asymptotically-large networks: (a) Cooperative jamming (b) Network coding

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66 Electrical and Computer Engineering Gupta-Kumar: n nodes each can share bits per second. Want to achieve this throughput securely, in the presence of m eavesdroppers of unknown location. Focus (as always): Avoiding the known eavesdropper location assumption. n good guys (matched into pairs) m bad guys. Secure throughput per pair? For what m? Problem: Secrecy Sca ling Asymptotically-large networks: (a) Cooperative jamming (b) Network coding

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67 Electrical and Computer Engineering Network (random extended network): Nodes are placed in the interval [0, n]. Legitimate nodes randomly placed: Poisson with unit density (n good guys on average) Eavesdroppers Poisson with e (n) ( m(n) = e (n) n bad guys on average.) n nodes matched into source- destination pairs uniformly at random. 1-D Networks (worst-case topology) S1S1 D1D1 D2D2 S2S2 n randomly located nodes -> how much secret information in the presence of m(n) eavesdroppers ? Asymptotically-large networks: (a) Cooperative jamming (b) Network coding

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68 Electrical and Computer Engineering A single eavesdropper of known location -> 1-D disconnected (zero secret bits)! Why? For any node to Eve’s left, Eve is closer (has larger SINR) than the good nodes located to Eve’s right. What to do? Answer: Nodes help each other to achieve secrecy -> Cooperation. × A EB B: Weaker signalE: Stronger signal Cooperative Jamming: EB B: Weaker signal, weaker noise E: Stronger signal, stronger noise J A 1-D Networks (worst-case topology) SD Eve Asymptotically-large networks: (a) Cooperative jamming (b) Network coding

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69 Electrical and Computer Engineering So, the idea to connect each S-D pair through a sequence of many single-cell hops + one multi-hop jump until reaching D. Routing Algorithm: ××× But what if you don’t know where the eavesdroppers are? Asymptotically-large networks: (a) Cooperative jamming (b) Network coding Jamming works if you know where the eavesdroppers are.

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70 Electrical and Computer Engineering ××× Unknown Eavesdropper Locations: I know how to protect the message if eavesdroppers are spaced far apart. But this time eavesdroppers can be anywhere. ×××××× kth cell (k+10)th cell Asymptotically-large networks: (a) Cooperative jamming (b) Network coding

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71 Electrical and Computer Engineering S D x: the b-bit secret message. S generates t-1 b-bit packets w 1, w 2, …, w t-1 randomly, sets w t to be such that x = 1 0 0 1 1 w 1 = 0 1 0 1 1 w 2 = 1 0 1 1 1 w 3 = 0 0 0 1 0 w 4 = 0 1 1 0 1 Solution comes with secret sharing at the source random Anyone who has all t packets has the message. Anyone who misses at least one packet has no information about the message. For one message, S sends t packets. The packets are sent in separate transmissions. Idea: Ensure an eavesdropper anywhere in the network misses at least one packet. Asymptotically-large networks: (a) Cooperative jamming (b) Network coding

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72 Electrical and Computer Engineering ×××××× Divide the network into regions: Coloring the network! Unknown Eavesdropper Location s: Asymptotically-large networks: (a) Cooperative jamming (b) Network coding

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73 Electrical and Computer Engineering Secrecy Analysis: The only potentially unsecure places: start or the end of a route. Near-eavesdropper n/logn eavesdroppers Standard Scheduling applied: cells take turns in transmissions: throughput per node pair (standard). Throughput Analysis: ××× S Asymptotically-large networks: (a) Cooperative jamming (b) Network coding

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74 Electrical and Computer Engineering (Insecure) Throughput: bits per second (per- node throughput) [Gupta-Kumar, 2001] bits per second (per-node throughput [Franceschetti et al, 2007] Multi-hop route connecting source- destination pairs. Two-Dimensional Networks (Review) If eavesdropper locations are known: Can route around the “holes” as long as m = o(n/logn) [Koyluoglu et al, 2011] Also: Securing each hop individually is sufficient to secure the end-to-end route [Koyluoglu et al, 2011] Asymptotically-large networks: (a) Cooperative jamming (b) Network coding

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75 Electrical and Computer Engineering Unknown eavesdropper location. What to do? First answer: Try Cooperative Jamming. At each hop, some nodes transmit artificial noise to protect the message from eavesdroppers around. BJ A Can tolerate m(n) = log n eavesdroppers (only). Is this the cost of unknown eavesdropper positions? Asymptotically-large networks: (a) Cooperative jamming (b) Network coding Two-Dimensional Networks [Vasudevan et al, 2011]

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76 Electrical and Computer Engineering x = 1 0 0 1 1 w 1 = 0 1 0 1 1 w 2 = 1 0 1 1 1 w 3 = 0 0 0 1 0 w 4 = 0 1 1 0 1 Two-Dimensional Networks (Secret Sharing) random Asymptotically-large networks: (a) Cooperative jamming (b) Network coding An eavesdropper cannot be close to many paths at once… Except when close to the source or the destination. [Capar, Goeckel, Towsley, 2012] Can tolerate n/logn eavesdroppers.

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77 Electrical and Computer Engineering What about those near eavedroppers? Problem: near eavesdropper (SNR gap). We know how to address that: Two-way scheme ( evens out the SNR gap ) Remember, the problem here was: Near eavesdropper of unknown location. Asymptotically-large networks: (a) Cooperative jamming (b) Network coding

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78 Electrical and Computer Engineering Secure Network Coding A formal way to study a wiretap network. Start with a given graph representing the network. Some of the edges are tapped. s d a b Gives necessary and sufficient condition to go securely from s to d, and (if possible) tells you how to do it. Nice formal way to check secrecy capability, but wireless secrecy: we don’t have a graph. Tapped! [Cai and Yeung, 2002], [Jain 2004]

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79 Electrical and Computer Engineering Secrecy Graph: Wireless Network -> Wiretap Graph Takes your wireless network, puts out a graph. Start with given locations of good guys {x i }, and bad guys {y i }. Then, a simple rule. × × Baseline graph × × Draw an edge from x i to x j if within radius. Edge (x i, x j ) is tapped if d(x i, y k ) ≤ d(x i, x j ) × tapped × secure [Haenggi, 2008]

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80 Electrical and Computer Engineering Toy Example 1 (Basic Two-way Scheme). An incoming connection can be very useful. This simple trick has an important implication for wireless secrecy. Two-way helps address the near eavesdropper problem 1) d generates a random message k and sends it to s. 2) s replies with (k is used as a one-time pad.) 3) d extracts x from c, k. e misses k, cannot decode x. Two nodes + one eavesdropper e catches whatever s says. An incoming secure edge is sufficient for secrecy.

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81 Electrical and Computer Engineering Toy Example 2: s disconnected from both neighbors in both directions! Still hope? Disconnected! Four nodes on the corners of a square. Two eavesdroppers in the middle of two edges.

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82 Electrical and Computer Engineering Toy Example 2 (continued): s disconnected from both neighbors in both directions! Still hope? 1)a generates, sends k1, b generates, sends k2. 2)s replies with 3) d gets c, k1, k2 -> extracts x e1 misses k2, e2 misses k1 s blocked from both sides. Can still achieve secrecy if these blockages are due to separate non-collaborating eavesdroppers. e1 catches whatever a or s says. e2 catches whatever b or s says.

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83 Electrical and Computer Engineering Back to Secrecy Capacity for the Main Result. Problem: near eavesdropper (SNR gap). We know how to address that: Two-way scheme ( evens out the SNR gap ) Remember, the problem here was: Near eavesdropper of unknown location.

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84 Electrical and Computer Engineering Two-Dimensional Networks S again generates four packets w1, w2, w3, w4. But this time, does the two-way scheme with four relays to deliver these packets. Any Eve here misses k2 -> misses w2 Draining Phase: How we initiate at the source Routing Algorithm: Draining, routing, delivery No Eve can be in between for all four r-s pairs. Asymptotically-large networks: (a) Cooperative jamming (b) Network coding [Capar and Goeckel, 2012]

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85 Electrical and Computer Engineering Two-Dimensional Networks Any Eve here misses k2 -> misses w2 Come from four directions. No Eve can be in between for all four r-s pairs. Asymptotically-large networks: (a) Cooperative jamming (b) Network coding Result: Network can tolerate any number of eavesdroppers of arbitrary location at the Gupta-Kumar per-pair throughput. Note: Importantly, the same technique can be used in practical networks that are: 1.sufficiently dense 2.add infrastructure

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86 Electrical and Computer Engineering Outline 1.Computational and Information Theoretic security basics 2.Potential solutions 3.Asymptotically-large networks 4.Undetectable communications (LPD) a.Emerging approaches for wireless channels b.Experiments 5.Current and Future Challenges

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87 Electrical and Computer Engineering LPD Communications – of our interest Problem: conceal presence of the message: “metadata” as opposed to concealing message content (encryption) Why? Lots of applications… Encrypted data looks suspicious “Camouflage” military operations etc… LPD=“low probability of detection” Limit adversary’s detection capability to tolerable level Fundamental limits of LPD communication LPD Communications: (a) Emerging approaches (b) Experiment From: The Guardian

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88 Electrical and Computer Engineering Scenario Alice uses radio to covertly communicate with Bob They share a secret key Willie attempts to detect if Alice is talking to Bob Willie is passive, doe’t actively jam Alice’s channel Willie’s problem: dee LPD Communications: (a) Emerging approaches (b) Experiment

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89 Electrical and Computer Engineering Scenario Alice uses radio to covertly communicate with Bob They share a secret key Willie attempts to detect if Alice is talking to Bob Willie is passive, doesn’t actively jam Alice’s channel LPD Communications: (a) Emerging approaches (b) Experiment

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90 Electrical and Computer Engineering Alice uses radio to covertly communicate with Bob They share a secret key Willie attempts to detect if Alice is talking to Bob Willie is passive, doesn’t actively jam Alice’s channel Willie’s problem: detect Alice Alice’s problem: limit Willie’s detection schemes Bob’s problem: decode Alice’s message or? Thanks! Scenario LPD Communications: (a) Emerging approaches (b) Experiment

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91 Electrical and Computer Engineering Results from Steganography: Problem: Modify characters in a cover text (message, picture, etc.) to convey secret message without detection. Results: 1. symbols can be modified in a cover text of length n symbols without detection. 2. bits of information can be encoded in those n symbols without detection But this is on a finite alphabet channel. What about a physical (e.g. wireless) channel? LPD Communications: (a) Emerging approaches (b) Experiment Covert Message

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92 Electrical and Computer Engineering Spread Spectrum LPD Communications: (a) Emerging approaches (b) Experiment f X(f) Original Spectrum Spread-Spectrum Signal “Hide signal in the noise” at a spectrum loss of 1/N (the bandwidth expansion or processing gain). But what is the fundamental tradeoff?

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93 Electrical and Computer Engineering Channel Model decode transmit i.i.d. Key K (codebook) You can modify every symbol (at low power) without detection, so the converse from steganography does not hold. LPD Communications: (a) Emerging approaches (b) Experiment

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94 Electrical and Computer Engineering The Detection Side (Willie): ROC Curves LPD Communications: (a) Emerging approaches (b) Experiment P(False Alarm ) = α 1-P(Miss) = 1-β Characterization of Willie’s detector: 1. Low threshold: always say “Yes”. 1. 2. 2. High threshold: always say “No”. 3. Tradeoff curve for an “average” detector. 3. Goal: Drive Willie to Curve “C”, useless detector. [from “circ.ahajournals.org”]

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95 Electrical and Computer Engineering Main Result: The Square Root Law Consider a party Alice trying to communicate to Bob in the presence of a Warden Willie, with all channels AWGN: 1.Alice can send bits reliably to Bob with probability of detection at Willie 0. 2.Conversely, if Alice tries to send bits to Bob, one of the following occurs: Bob’s decoding error is bounded away from zero, or Alice’s transmission is detected with probability 1. or? Thanks! [Bash, Goeckel, Towsley, 2013] LPD Communications: (a) Emerging approaches (b) Experiment

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96 Electrical and Computer Engineering Structure of the proof Achievability + Willie doesn’t detect transmission, despite a detector, and + Bob decodes the message reliably with a (possibly) sub- optimal scheme Converse + Bob cannot decode the message with an optimal detector, or + Willie can detect the transmission with a sub-optimal scheme or? Thanks! LPD Communications: (a) Emerging approaches (b) Experiment

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97 Electrical and Computer Engineering Achievability: Construction Random codebook with average symbol power Codebook revealed to Bob, but not to Willie Willie knows how codebook is constructed, as well as n and System obeys Kerckhoffs’s Law: all security is in the key used to construct codebook 00000··· W1W1 00001 W2W2 00010 W3W3 11111 W2MW2M 2M2M M-bit messages x 11 x 12 x 13 x 1n ··· c(W 1 ) x 21 x 22 x 23 x 2n ··· c(W 2 ) x 31 x 32 x 33 x 3n ··· c(W 3 ) x2M1x2M1 ··· c(W 2 M ) x2M2x2M2 x2M3x2M3 x2Mnx2Mn n-symbol codewords Each symbol i.i.d.

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98 Electrical and Computer Engineering Achievability: Analysis of Willie’s Detector Willie collects n observations -- distribution when Alice quiet, -- distribution when Alice transmitting, For any hypothesis test: Bounding Willie’s detection: Total Variation: 1-norm distance on the distributions Relative entropy LPD Communications: (a) Emerging approaches (b) Experiment

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99 Electrical and Computer Engineering Back of the Envelope Hence, the number of bits conveyed in n symbols is: (That is not quite rigorous, as Shannon capacity is for a fixed R as n goes to infinity.) But there is a simple workaround to finish the proof. LPD Communications: (a) Emerging approaches (b) Experiment

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100 Electrical and Computer Engineering Converse When Alice tries to transmit bits in n channel uses, using arbitrary codebook, either Detected by Willie with arbitrarily low error probability Bob’s decoding error probability bounded away from zero Two step proof: 1.Willie detects arbitrary codewords with average symbol power using a simple power detector 2.Bob cannot decode codewords that carry bits with average symbol power with arbitrary low error LPD Communications: (a) Emerging approaches (b) Experiment

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101 Electrical and Computer Engineering LPD Communications: (a) Emerging approaches (b) Experiment Done at Raytheon/BBN Technologies with collaborator Saikat Guha Experiment: given possible slots for PPM symbols, Alice and Bob secretly agree on a random subset of expected size to use for message transmission Bob ignores the “empty” symbols, but Willie cannot since he doesn’t know where they are Alice transmits: Bob receives: Willie receives: - transmitted pulses- dark clicks

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102 Electrical and Computer Engineering LPD Communications: (a) Emerging approaches (b) Experiment Alice (laser) Variable attenuat or Eve (SPD) Bob (SPD) PBSC HWP Collimator Mirror Linear polarizer Experimental Set-Up Fiber-Beam Splitter Fiber-Beam Splitter Alice BobWillie

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103 Electrical and Computer Engineering LPD Communications: (a) Emerging approaches (b) Experiment Credit for the setup: Andrei Gheorghe (Amherst College), Jon Habif (BBN) and Monika Patel (BBN)

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104 Electrical and Computer Engineering BobWillie P(dark click) 4.6e -6 8.2e- 5 P(miss pulse) 0.250.97 c 0.25 PPM order 32 R/S code rate 1/2 Number of PPM slots used Bits received Each data point is average of 100 runs Preliminary Data - Bob LPD Communications: (a) Emerging approaches (b) Experiment

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105 Electrical and Computer Engineering Preliminary Data - Willie Number of PPM slots used Willie’s min probability of error Each data point is computed from the maximum vertical distance between empirical ROC curve and diagonal based on 100 runs LPD Communications: (a) Emerging approaches (b) Experiment

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106 Electrical and Computer Engineering Other Recent Advances in LPD Communications For Binary Symmetric Channels (BSCs): 0 0 11 1-p B pBpB pBpB 0 0 11 1-p W pWpW pWpW Bob’s Channel (p B :prob of error)Willie’s Channel (p W :prob of error) If p B >p W (Bob is closer): can get bits without shared codebook. 1. No Shared Codebook [Che, Bakshi, Jaggi, 2013]

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107 Electrical and Computer Engineering 2. If Willie does not know the time of the message: Slot 0Slot 1Slot 2Slot 3Slot T nnnnn Can transmit bits in n channel uses. Other Recent Advances in LPD Communications (For example, Alice-to-Bob secret: “I will send the message at 4:23pm today.”) Willie has to watch a much larger time interval. [Bash, Goeckel, Towsley, 2014]

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108 Electrical and Computer Engineering Outline 1.Computational and Information Theoretic security basics 2.Potential solutions 3.Asymptotically-large networks 4.Undetectable communications (LPD) 5.Current and Future Challenges

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109 Electrical and Computer Engineering Challenges 1.Exploiting when Alice -> Bob channel is better than Alice -> Eve Challenge: unknown Eve location 2.Exploiting common randomness of channel reciprocity Challenge: limited number of key bits 3.Exploiting “public discussion” Challenge: two-way communication and unknown Eve 4.Attacking Eve’s receiver hardware Challenge: short range, assumptions on Eve’s hardware 5. Interference Cancellation Challenge: near-far environment 6.Relay Chattering Challenge: great in theory, not so much in practice (density of nodes). Is the Network the Solution?

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110 Electrical and Computer Engineering Challenges for the Future 1. Biggest question: Is information-theoretic security in wireless just a waste of (mostly academic) resources? There are certainly lots of doubters: 1.“My problem with IT security is you can’t guarantee it.” -Andrew Worthen, MIT-LL 2.“If cryptographic security primitives are broken, the world collapses with or without IT security.” -Dakshi Agrawal, IBM-Watson 3.… Is it only used in a defense-in-depth approach under cryptographic stuff? But then is there really value-added? 2. Undetectable Communications: Can we build “shadow networks”?

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